Merge branch 'SethPoulsen-proof-blocks'

Author: bnmnetp

runestone/parsons/js/dagGrader.js

@@ -0,0 +1,123 @@
+import LineBasedGrader from "./lineGrader";
+import { DiGraph, hasPath, isDirectedAcyclicGraph } from "./dagHelpers";
+
+function graphToNX(answerLines) {
+  var graph = new DiGraph();
+  for (let line1 of answerLines) {
+    graph.addNode(line1.tag);
+    for (let line2tag of line1.depends) {
+      // the depends graph lists the *incoming* edges of a node
+      graph.addEdge(line2tag, line1.tag);
+    }
+  }
+  return graph;
+}
+
+function isVertexCover(graph, vertexCover) {
+  for (let edge of graph.edges()) {
+    if (!(vertexCover.has(edge[0]) || vertexCover.has(edge[1]))) {
+      return false;
+    }
+  }
+  return true;
+}
+
+// Find all subsets of the set using the correspondence of subsets of
+// a set to binary string whose length are the size of the set
+function allSubsets(arr) {
+  let subsets = {};
+  for (let i = 0; i <= arr.length; i++) {
+    subsets[i] = [];
+  }
+  for (let i = 0; i < Math.pow(2, arr.length); i++) {
+    let bin = i.toString(2);
+    while (bin.length < arr.length) {
+      bin = "0" + bin;
+    }
+    let subset = new Set();
+    for (let j = 0; j < bin.length; j++) {
+      if (bin[j] == "1") {
+        subset.add(arr[j]);
+      }
+    }
+    subsets[subset.size].push(subset);
+  }
+  return subsets;
+}
+
+export default class DAGGrader extends LineBasedGrader {
+  inverseLISIndices(arr, inSolution) {
+    // For more details and a proof of the correctness of the algorithm, see the paper: https://arxiv.org/abs/2204.04196
+
+    var solution = this.problem.solution;
+    var answerLines = inSolution.map((block) => block.lines[0]); // assume NOT adaptive for DAG grading (for now)
+
+    let graph = graphToNX(solution);
+
+    let seen = new Set();
+    let problematicSubgraph = new DiGraph();
+    for (let line1 of answerLines) {
+      for (let line2 of seen) {
+        let problematic = hasPath(graph, {
+          source: line1.tag,
+          target: line2.tag,
+        });
+        if (problematic) {
+          problematicSubgraph.addEdge(line1.tag, line2.tag);
+        }
+      }
+
+      seen.add(line1);
+    }
+
+    let mvc = null;
+    let subsets = allSubsets(problematicSubgraph.nodes());
+    for (let i = 0; i <= problematicSubgraph.numberOfNodes(); i++) {
+      for (let subset of subsets[i]) {
+        if (isVertexCover(problematicSubgraph, subset)) {
+          mvc = subset;
+          break;
+        }
+      }
+      if (mvc != null) {
+        break;
+      }
+    }
+
+    let indices = [...mvc].map((tag) => {
+      for (let i = 0; i < answerLines.length; i++) {
+        if (answerLines[i].tag === tag) return i;
+      }
+    });
+    return indices;
+  }
+
+  checkCorrectOrdering(solutionLines, answerLines) {
+    if (!isDirectedAcyclicGraph(graphToNX(solutionLines))) {
+      throw "Dependency between blocks does not form a Directed Acyclic Graph; Problem unsolvable.";
+    }
+
+    let seen = new Set();
+    let isCorrectOrder = true;
+    this.correctLines = 0;
+    this.solutionLength = solutionLines.length;
+    let loopLimit = Math.min(solutionLines.length, answerLines.length);
+    for (let i = 0; i < loopLimit; i++) {
+      let line = answerLines[i];
+      if (line.distractor) {
+        isCorrectOrder = false;
+      } else {
+        for (let j = 0; j < line.depends.length; j++) {
+          if (!seen.has(line.depends[j])) {
+            isCorrectOrder = false;
+          }
+        }
+      }
+      if (isCorrectOrder) {
+        this.correctLines += 1;
+      }
+      seen.add(line.tag);
+    }
+    return isCorrectOrder;
+  }
+}